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compared to the cerebellum were estimated using a simplified reference region
model24,25. The model derives BP from the ratio of the volumes of distribution
of the ligand in the striatum relative to the cerebellum. BP is a composite
function of parameters, as follows:
BP ¼
f 2 Bmax
K DTracer 1 þ
Fi
K Di
^
i
!
where Bmax is the total concentration of specific binding sites, KDTracer the
equilibrium dissociation constant of the ligand, f2 is the ‘free fraction’ of
unbound ligand in the tissue, and Fi and KDi are the concentrations and
equilibrium dissociation constants, respectively, of i competing endogenous
ligands. Changes in BP are attributed to changes in Fi for endogenous
dopamine. Striatal ROIs were outlined on an add-image of summated time
frames, using an edge-fitting algorithm set at a fixed threshold (40%) of the
image maximum. The ventral (comprising the ventral half of the putamen) and
dorsal (comprising the dorsal half of the putamen and the body of the caudate
nucleus) striata were operationally defined. The cerebellum was defined by
cluster analysis26. BP and RI values were calculated for the striatal ROIs using the
TACs for [11C]RAC binding up to 50 min after injection25. Differences in
[11C]RAC-BP at baseline and during the task were tested with repeatedmeasure ANOVA, with three ‘within-subject’ factors (task versus baseline,
left versus right hemisphere and dorsal versus ventral striatum). Spearman rank
correlation coefficients were calculated for the relationship between changes in
[11C]RAC-BP and the highest performance level during the game for each ROI.
11
SPM analysis. Parametric images of [ C]RAC-BP24 were analysed using
11
SPM96 (ref. 21). The [ C]RAC-RI images were used to define the stereotactic
transformation parameters for the [11C]RAC-BP images. Contrasts of the
condition effects at each voxel of the [11C]RAC-BP images were assessed
using the t-value, with the highest performance level entered as a covariate of
interest, giving a statistical image for each contrast.
Received 23 September 1997; accepted 20 March 1998.
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accumbens dopamine release increases during instrumental level pressing for food but not free food
consumption. Pharmacol. Biochem. Behav. 49, 651–660 (1994).
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transmission elicited by food reinforcement: an electrochemical study in rat. J. Neurosci. 16, 8160–
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synaptic transmission using PET: a review of relevant neurophysiology. Hum. Brain Mapp. 3, 24–34
(1995).
13. Morris, E. D., Fisher, R. E., Alpert, N. M., Rauch, S. L. & Fischman, A. J. In vivo imaging of
neuromodulation using positron emission tomography: optimal ligand characteristics and task
length for detection of activation. Hum. Brain Mapp. 3, 35–55 (1995).
14. Graybiel, A. M., Aosaki, T., Flaherty, A. W. & Kimura, M. The basal ganglia and adaptive motor
control. Science 265, 1826–1831 (1994).
15. Schultz, W. Dopamine neurons and their role in reward mechanisms. Curr. Opin. Neurobiol. 7, 191–
197 (1997).
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1–13 (1995).
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brain. J. Nucl. Med. 34, 609–613 (1993).
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kinetic analysis of PET data. J. Cereb. Blood Flow Metab. 14, 995–1010 (1994).
19. Endres, C. J. et al. Kinetic modelling of [11C]raclopride: combined PET-microdialysis studies. J. Cereb.
Blood Flow Metab. 9, 932–942 (1997).
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and dopamine in the prefrontal cortex of the rat. Neurosci. Lett. 177, 83–86 (1993).
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Brain Mapp. 2, 189–210 (1995).
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dopaminergic system by stress. Nature 263, 242–244 (1976).
23. Wise, R. A. The dopamine synapse and the notion of ‘‘pleasure centres’’ in the brain. Trends Neurosci.
3, 91–94 (1980).
24. Gunn, R. N., Lammertsma, A. A., Hume, S. P. & Cunningham, V. J. Parametric imaging of ligandreceptor binding in PET using a simplified reference region model. Neuroimage 6, 279–287 (1997).
25. Lammertsma, A. A. & Hume, S. P. Simplified reference tissue model for PET receptor studies.
Neuroimage 4, 153–158 (1996).
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Using PET (eds Myers, R., Cunningham, V., Bailey, D. & Jones, T.) 301–306 (Academic, London,
1996).
Acknowledgements. M.J.K. was supported by a grant from the Theodore and Vada Stanley Foundation
Research Program; R.N.G., V.J.C., D.J.B. and P.M.G. were supported by the Medical Research Council; and
A.D.L. was supported by a fellowship from the British Brain and Spine Foundation. We thank P. Dayan
and L. Farde for discussions and comments on the manuscript; and K. Friston, A. Holmes and
J. Ashburner for statistical advice and help with the SPM analysis.
Correspondence and requests for materials should be addressed to P.M.G. (e-mail: [email protected].
uk).
Theroleofdendritesinauditory
coincidence detection
Hagai Agmon-Snir*, Catherine E. Carr† & John Rinzel*‡
* Mathematical Research Branch, NIDDK, National Institutes of Health,
Bethesda, Maryland 20892, USA
† Department of Zoology, University of Maryland, College Park,
Maryland 20742, USA
.........................................................................................................................
Coincidence-detector neurons in the auditory brainstem of mammals and birds use interaural time differences to localize
sounds1,2. Each neuron receives many narrow-band inputs from
both ears and compares the time of arrival of the inputs with an
accuracy of 10–100 ms (refs 3–6). Neurons that receive lowfrequency auditory inputs (up to about 2 kHz) have bipolar
dendrites, and each dendrite receives inputs from only one
ear7,8. Using a simple model that mimics the essence of the
known electrophysiology and geometry of these cells, we show
here that dendrites improve the coincidence-detection properties
of the cells. The biophysical mechanism for this improvement is
based on the nonlinear summation of excitatory inputs in each of
the dendrites and the use of each dendrite as a current sink for
inputs to the other dendrite. This is a rare case in which the
contribution of dendrites to the known computation of a neuron
may be understood. Our results show that, in these neurons, the
cell morphology and the spatial distribution of the inputs enrich
the computational power of these neurons beyond that expected
from ‘point neurons’ (model neurons lacking dendrites).
Over the past 40 years it has become widely accepted that
dendrites play a major role in neuronal computation9. Despite
intensive efforts to decipher this role10–16, however, the contribution
of the dendrites to the function of the single neuron remains elusive.
Nevertheless, the existence of different dendritic geometries and
their plausible effect on computation have been used as evidence for
dendritic computation11,12,17. As analysis of dendritic computation is
most powerful when the role of the neuron is understood, we used
brainstem auditory coincidence detectors to demonstrate the computational advantages of having synaptic inputs on the dendrites
rather than on the cell body.
Coincidence detectors of the auditory brainstem are binaural
neurons that respond maximally when they receive simultaneous
inputs from the two ears. This condition is met when delay line
inputs from each ear exactly compensate for a delay introduced by
an interaural time difference (ITD, the time difference between the
‡ Present address: New York University, Center for Neural Science and Courant Institute of Mathematical
Sciences, New York 10003, USA.
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Figure 1 A point-neuron model for auditory coincidence detectors. a, Avian (top)
and mammalian (bottom) low-frequency coincidence detector neurons. The
stimulus frequency of the chicken nucleus laminaris cells increases from left to
right (adapted from refs 7, 30). The bipolar architecture and the segregation of the
inputs from both ears is common to both mammalian and avian coincidence
detectors. b, Superimposed voltage responses during application of subthreshold and suprathreshold current steps to nucleus laminaris neurons20.
8
c, Responses of the point-neuron model to step current injections (see Methods).
The output of the coincidence detector is phase-locked to their inputs (with some
jitter; Fig. 2b). d, ITD curve in response to 1 kHz stimulus frequency shows that the
point-neuron model performs like coincidence detectors in mammals and
birds3,4,6,20.
two ears)1–4. These coincidence-detector neurons are particularly
suitable for an analysis of dendritic function. First, they have
stereotyped bipolar dendrites (Fig. 1a)7,8. Second, the inputs from
each ear are segregated on the dendrites, with inputs from the
ipsilateral ear terminating on the dorsal dendrites and inputs from
the contralateral ear on the ventral dendrites7,8. Third, the length of
the dendrites increases with decreasing best frequency of the sound
stimulus in the chick7,18 (Fig. 1a), suggesting a computational role
for the dendrites. Fourth, the electrophysiological properties of
these neurons have been well characterized19,20. As is appropriate for
timing devices, these coincidence detectors do not respond to slowly
varying inputs and fire one or few spikes in response to a step
current injection (Fig. 1c).
We used data from the neurons of the ITD circuit to construct a
minimal biophysical model that mimicked the essential properties
of the coincidence detectors (Fig. 1b, c; see Methods)4,19–22. This
model, like earlier models23–26, detected coincidences when inputs
from both ears arrived directly at its soma (Fig. 1d). In the present
model, however, we were able to investigate the contribution of
dendrites. We modelled two simple dendrites as unbranched cables
(electronic length, 0.2 l), on the basis of measured dendritic lengths
and the biophysical properties of the coincidence detectors (see
Methods)7,20. The model cell received 12 inputs, 6 from each ear. In
some cases, all 12 inputs were located on the soma, and in
a
other cases, all 6 inputs from the left ear were located on one
dendrite, 0.1 l from the soma, and all 6 from the right ear on the
other dendrite (Fig. 2a). The inputs were phase-locked (Fig. 2b; see
Methods).
When a sound moves around the head, there is a phase shift
between the two ears, and the response of the coincidence detector
varies in cyclic fashion between best ITD (maximum) and worst
ITD (minimum; Fig. 1d and 2c). Any mechanism that increases the
maximum and at same time decreases the minimum of these ITD
plots improves the detection of sound localization. Indeed, in model
ITD plots, the contrast between the maximal and minimal spike
rates was greater when the inputs from each ear were segregated and
located on the dendrites (Fig. 2c). This improvement in coincidence
detection produced by locating the inputs on the dendrites was
robust9. We showed this by changing the single (unitary) synaptic
conductance (USC) as a parameter for several different input
configurations, as maximal and minimal spike rates also depended
upon USC amplitude (Fig. 2d). For each configuration, maximum
and minimum spike rates increased with increasing synaptic conductance. Best coincidence detection (Fig. 2d, dotted line) was
achieved when the inputs were segregated on the dendrites, and
when the dendrites were thin (see Methods).
This improvement in ITD coding is based on local computation
at the dendrites. In general, synaptic inputs sum nonlinearly,
b
Left
Figure 2 A bipolar-neuron model for coincidence
Model of the input trains
Model of the coincidence detector
detection. a, The bipolar-neuron model consists of a
Stimulus
Right
soma (centre) and two cylindrical dendrites (see
Methods). b, Inputs resembled in vivo inputs (see
Input train 1
Methods). c, Model ITD curves for a 500-Hz stimulus
showed an improvement in ITD coding when dendrites
were added (0.2-l thick (4 mm) passive dendrites). The
Input train 2
contrast between the maximum spike rate (08 delay) and
the minimum spike rate (1808 delay) was larger when the
Input train 3
c
150
Min response (Hz)
150
100
50
Min response
0
180
Phase shift (degr
ees)
NATURE | VOL 393 | 21 MAY 1998
360
maximum and minimum spike rates as the USC
changes. Dashed line, inputs on soma, USC range
0.007–0.011 mS; solid line inputs on thick (4 mm diameter)
100
dendrites, USC range 0.013–0.024 mS; dotted line, inputs
on thin (2 mm diameter) dendrites, USC range 0.014–
50
0.026 mS. Dendritic USCs were made larger than somatic
0
-180
(dashed line; USC ¼ 0:01 mS). d, Parametric plot of different input configurations shows the relationship between
Max response
200
Firing rate (Hz)
USC ¼ 0:022 mS), compared with the point-neuron model
d
250
0
-360
inputs were segregated on the dendrites (solid line;
USCs to provide similar maximum responses.
150
175
200
225
Max response (Hz)
Nature © Macmillan Publishers Ltd 1998
269
letters to nature
because the driving force for excitatory synaptic currents decreases
with depolarization. Hence, the net synaptic current from several
inputs arriving simultaneously at nearby sites on the same dendrite
is smaller than the current generated if these inputs arrive at
different dendrites9. Figure 3a illustrates how the segregation
helps to improve coincidence detection. Thus, the conductance
threshold, or minimum synaptic conductance needed to trigger a
somatic action potential, is higher when the synaptic events are on
the same dendrite, compared with when they are split between the
bipolar dendrites. In the bipolar model, when the inputs are
segregated and the phase shift is 08, inputs arrive simultaneously
at both dendrites and it is comparably easy to generate an action
potential. When the phase shift is 1808, at every half cycle inputs
arrive on only one dendrite and the conductance threshold is large.
In the point neuron, however, the conductance threshold does not
vary when the phase shifts are 08 and 1808. Thus, the difference
between the firing rates in the 08 and the 1808 phase shift cases is
larger for the bipolar neuron with segregated inputs than for the
point neuron.
Action-potential thresholds depended on whether the inputs
were on the cell body or the dendrites (Fig. 3b). We used the
concept of conductance threshold to explain the difference between
segregated and non-segregated inputs. For each model configuration, points above the curve represent combinations of suprathreshold synaptic inputs from left ( gL) and right ( gR) ears. When
binaural inputs arrive at the same location, action potentials fire
when g L þ g R is larger than a fixed conductance threshold (Fig. 3b,
straight dashed line). Conductance-threshold plots are not linear
when the inputs from each ear are segregated on different dendrites.
We used the biophysical model to calculate these thresholds and
show that the conductance threshold ( g L þ g R ) for equally distributed inputs (g L ¼ g R ; points I and II in Fig. 3b) is smaller than the
threshold (gTh) for inputs arriving from only one side ( g L ¼ 0 or
g R ¼ 0; points III and IV). Thus, the model cell was most likely to
fire action potentials when stimulated by coincident inputs from
each ear.
As dendritic length varied with best frequency in the chicken7, we
also investigated the effects of stimulus frequency and dendritic
length on coincidence detection. The performance of the model
(Fig. 2d) deteriorated with inputs of higher frequencies (Fig. 3c; the
curves for higher frequencies were to the left of those of lower
frequencies, reflecting poorer coincidence detection). Furthermore,
at higher frequencies the contrast between the maximum and
minimum spike rates did not change much when the inputs were
on the dendrites. The main reason for the reduction in dendritic
advantage at higher stimulus frequencies was input jitter. At higher
frequencies, jitter resulted in an overlap in time between inputs
from both ears, even when there was a 1808 phase shift between
them. The effect of this overlap on the conductance threshold was
comparably large when the inputs were on the dendrites; even a
small ‘erroneous’ input from one ear significantly lowered the
conductance threshold for the inputs from the other ear (compare,
for example, points III and V in Fig. 3b). As a result, at high
frequencies the firing rate in the 1808 mode could be even larger
than in the somatic model, making the dendrites a burden instead of
an advantage. This prediction of a negligible dendritic length
required to detect higher frequencies conforms to the observation
of short dendrites on high-frequency-coincidence detectors in
chickens7.
From this analysis, we understood that in the presence of jitter,
IV
1
b
gL/gTh
a
Phase shift: 0˚
II
L
I
R
V
0
c
0
III
1
gR/gTh
d
Phase shift: 180˚
750Hz
Min response (Hz)
50
L
R
500Hz
1000Hz
25
0
0
50
100
150
200
250
Max response (Hz)
Figure 3 Biophysical mechanism and frequency dependence. a, The role of
arriving from only one side, however, would not fire the cell, and the 1808 firing rate
nonlinear integration of synaptic inputs in enhancement of coincidence detection
would be smaller. b, Schematic threshold lines for different input configurations.
is explained in a schematic diagram. The sinusoidal stimulus (top curve) leads to
Using the biophysical model, we calculated thresholds for the cases of Fig. 2d
a binomially distributed random number of synaptic events from the left (L) and
(triangles, thick dendrites; diamonds, thin dendrites). gTh is defined as the
right (R) ears at every cycle (depicted as stacks of blocks). Suppose that six
conductance threshold for inputs arriving from only one side. We fitted those
simultaneous synaptic events were just enough to trigger a postsynaptic spike in
points to the equation gaL þ gaR ¼ gaTh , and good fit was obtained for a ¼ 0:77 and
the point neuron. More firings must occur when the phase shift is 08 than when it
0.48, respectively. The straight line therefore represents the case a ¼ 1. c, The
is 1808 (in the example, six spikes in the 08 case and three in the 1808 case). In the
effect of frequency on coincidence detection in the biophysical model. The
bipolar neuron, the USC can be adjusted so that the firing rate for phase shift of 08
minimum and maximum spike rates for the somatic and dendritic configurations
equals that of the point neuron. Hence, three inputs from the left arriving at the
are shown for three frequencies. The dendritic model is as in Fig. 2d with thin
same time as three inputs from the right would fire the bipolar cell. Six inputs
(2 mm diameter) dendrites.
270
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NATURE | VOL 393 | 21 MAY 1998
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letters to nature
severe nonlinear summation is a disadvantage. With long dendrites,
larger voltages were required at the dendritic site to trigger a spike at
the soma, as the opposite dendrite served as a current sink and the
voltage gradient from the dendritic site to the soma was steeper. As a
result, the summation of inputs at the dendritic site was more
nonlinear than for shorter dendrites, and could worsen the coincidence detection at high stimulus frequencies. For example, when
f stim ¼ 500 Hz, the best coincidence detection occurred when the
dendrites were about 0.4 l each, whereas optimal dendritic lengths
were shorter for higher frequencies.
A simple bipolar integrate-and-fire model that retained the
biophysical model’s essential features improved our understanding
of how the nonlinear summation on bipolar dendrites enhances
coincidence detection and why the optimal dendritic length was
shorter for higher frequencies. Suppose that, within a given stimulus cycle, left-ear afferents evoked a net synaptic input conductance
transient of size gL, and right-ear afferents evoked gR. In response,
the neuron fired with probability P( gL, gR). If the afferent inputs
arrived at a single site and if the noise-free neuron had a sharp fixed
threshold, then P ¼ 1 if g L þ g R > g Th and P ¼ 0 otherwise, where
gTh is the conductance threshold at this input site. When the inputs
were segregated on the bipolar dendrites, the nonlinear integration
of inputs seen in the biophysical model could be mimicked by using
the condition g aL þ g aR > g aTh , where a < 1 depended on the nonlinear integration at the dendrites (Fig. 3b). Assuming n afferents
from each ear, and independence between synaptic events in
different stimulus cycles and in different input trains, the probability, bi,n, that i synaptic events were delivered by one ear’s afferents
in a stimulus cycle could be approximated using a binomial
distribution. We calculated the probability for postsynaptic firing
in a stimulus cycle when there is no phase shift between the left and
right inputs (P0) and when the binaural phase shift is 1808 (P180);
these probabilities depend on gsyn, the USC (see Methods). The cell’s
mean firing rate is P0 fstim for the 08 phase shift case and P180 fstim for
the 1808 case. This simple analytical model yields results in qualitative agreement with those from our minimal biophysical model
(Fig. 4a). It embodies the combined essential effects due to randomness in the number of the synaptic events per cycle and the nonlinear
integration caused by the spatial distribution of the afferents.
The role of jitter was demonstrated in the integrate-and-fire
model by a simple modification. We assumed that in the 1808
phase shift case, a fraction, b, of the input conductance from one ear
might affect the integration of the inputs from the other ear (see
Methods). Analysis of the input trains of the biophysical model
showed that b is comparably small for f stim ¼ 500 Hz, whereas it can
approach 0.4 when f stim ¼ 1;000 Hz. In this modified model, coincidence detection was worse at higher frequencies, and the dendritic
advantage was diminished (Fig. 4b). Without considering jitter
(b ¼ 0 for all frequencies), putting inputs on dendrites (a , 1) was
advantageous even at high frequencies. Using the modified model
it was easy to demonstrate that when b was non-zero, there was
an optimal a for best coincidence detection (Fig. 4c). As longer
dendrities have smaller values of a, there is an optimal dendritic
length for each frequency, and this optimal length decreases
with higher frequencies. These predictions match the changes in
dendritic length observed in the chicken coincidence detectors7
(Fig. 1a).
We have shown how dendrites improve coincidence detection in
the cells of the auditory brainstem, using basic biophysical mechanisms to explain their computational role. One mechanism is the
segregation of the inputs on the dendrites, allowing nonlinear
integration between the inputs from left and right ears. The
second mechanism is a modulation of the nonlinearity of the
integration by using the dendrites as current sinks for each other.
The computational module isolated in the auditory coincidence
detectors might be used in other neurons with branched dendritic
trees, perhaps as part of a more complex computation. For example,
in cortical neurons, the segregation of inputs on the two main
branches of the pyramidal-cell apical tree might use a similar
computational module, with the same biophysical mechanism as
the brainstem auditory cells. The segregation of inputs on the many
basal dendrites might also be involved in such a mechanism. The
investigation of other cells with known functions could yield a set of
plausible ‘computational building blocks’ that might help to decipher the dendritic code in more complex cells with unknown
M
functions.
8
.........................................................................................................................
Methods
Figure 4 Bipolar integrate-and-fire model. a, Contrast enhancement in the
Point-neuron model. Data from nucleus magnocellularis and nucleus
integrate-and-fire model demonstrated with parametric plots for different input
laminaris cells were used to construct the model, which mimicked the
properties of coincidence detectors, including phase-locking to about
1.5 kHz19–22,27. The fast potassium currents (t , 1 ms) that repolarize the
cell were modelled, whereas slow potassium currents (t . 10 ms) were substituted by a steady-state conductance. The model equations were Morris–
Lecar type28,29: dV=dt ¼ ð 2 1=C m Þ½ḡ Na m` ðVÞðV 2 V Na Þ þ g syn ðV 2 V syn Þþ
ḡ K wðV 2 V K Þ þ g L ðV 2 V L Þ; dw=dt ¼ f½ðw` ðVÞ 2 wÞ=tw ðVÞÿ; where C m ¼
0:0147 nF, ḡ Na ¼ 33 nS, V Na ¼ 20 mV, V syn ¼ 0 mV, ḡ K ¼ 237 nS, V K ¼
2 70 mV, g L ¼ 7 ns, V L ¼ 2 62:5 mV, f ¼ 1:0, m` ðVÞ ¼ 1=½1 þ exp{ðV 2
V 1 ÞV 2 }ÿ=2, w` ðVÞ ¼ 1=½1 þ exp{ðV 2 V 3 Þ=V 4 }ÿ=2, tw ðVÞ ¼ 1=cosh{ðV 2
configurations (as in the biophysical model; Fig. 2d). We assumed 12 input lines, 6
from each side; f stim ¼ 500 Hz and f pre ¼ 350 Hz. b, The effect of jitter on coincidence detection for various frequencies is demonstrated in the modified
integrate-and-fire model. b ¼ 0 for 500 Hz, 0.15 for 750 Hz, and 0.3 for 1,000 Hz.
The dendritic (a ¼ 0:5) case for 750 Hz with b ¼ 0 is also shown. c, The effect of a
on coincidence detection in the modified integrate-and-fire model. f stim ¼ 750 Hz,
b ¼ 0:15. The optimal coincidence-detection properties are found here for a ¼ 0:6.
For a ¼ 0:2, coincidence detection is worse than for a ¼ 1, reflecting the loss of
dendritic advantage.
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V 5 Þ=V 6 }, and, in mV, V 1 ¼ 2 42:5, V 2 ¼ 2 1, V 3 ¼ 2 43:0, V 4 ¼ 2 4,
V 5 ¼ 2 60:0, and V 6 ¼ 64. Simulation results were obtained by numerical
integration of differential equations over 10 s.
Bipolar-neuron model. See Fig. 2a. The soma was the same as in the pointneuron model (20 mm diameter, Rsoma ¼ 135 MQ); the dendritic diameter was
either 4 mm (thick dendrites) or 2 mm (thin dendrites), with axial resistivity
Ri ¼ 200 Q cm and membrane resistance Rm ¼ 1;700 Q cm2. For a dendrite of
diameter 4 mm, l ¼ 290 mm, whereas for a dendrite of diameter 2 mm,
l ¼ 200 mm. Parameters were based on recordings from chicken coincidence
detectors20. Dendrites were modelled by 0.05-l-connected compartments and
had either active membrane (identical to the point neuron) or passive
membrane (voltage-dependent conductances fixed to their resting values).
Because synaptic inputs arrived at the cell in every cycle, it was insufficient to
use a simple threshold function to recognize action potentials in the somatic
response. We therefore added a long axon with a higher density of voltagedependent conductances. We counted only action potentials that propagated.
Synaptic-input model. See Fig. 2b. For every input train, at every stimulus
cycle, the probability of an input arriving was defined as fpre/fstim, where fstim was
the stimulus frequency and fpre (<fstim) was the average spike rate of the input
train. f pre ¼ 350 Hz for all stimulus frequencies27. The stimulus cycles were
regulated as independent events. To account for the jitter in the phase-locking
of the inputs to the stimulus, measured by vector strength (VS)3, we shifted
each input in time from the beginning of the cycle by a random variable t shift ,N
p
(m ¼ 0, j ¼ ð1;000=f stim Þ{ ½ 2 2lnðVSÞÿ=ð2pÞ}ms). For VS > 0:2, this resulted
in input trains with the required VS. Except in Fig. 1d, we used VS ¼ 0:7. In
Fig. 1d, VS ¼ 0:8. Synaptic inputs were rectangular conductance changes,
0.4 ms wide.
Bipolar integrate-and-fire model. The probability that the coincidencedetector neuron would fire in a given stimulus cycle was assumed to be
Pð g L ; g R Þ ¼ 1=ð1 þ exp½{1 2 ð g L =g Th Þa 2 ð g R =g Th Þa }=kÿÞ, where gL and gR were
the total synaptic input conductance during this cycle from the left and right
ears, respectively. We used k ¼ 0:05 and g Th ¼ 1 (the positive parameter k
determines the steepness of the sigmoid threshold function). By using a
sigmoid P( gL, gR) (rather than the condition g aL þ g aR > g aTh , which is equivalent
to the sigmoidal function when k approaches 0), we approximately accounted
for the effects of small intrinsic noise, jitter in a composite input, and a graded
threshold for the spike-generating
n mechanism. The probability bi,n (see text)
ð f pre =f stim Þi ð1 2 f pre =f stim Þn 2 i. Then, P0 is
was calculated by bi;n ¼
i
n
P0 ¼
n
^^
bi;n bj;n Pðig syn ; jg syn Þ
i¼0 j¼0
where input combinations are summed with index i for the left side and j for the
right. On the other hand, if the binaural phase shift was 1808, the probability to
fire during one cycle (that is, the probability that inputs from the left or the
right ear will cause firing) was approximated by
n
P180 ¼ 2
^b
i;n
Pðig syn ; 0Þ
i¼0
provided that P180 was small enough. In the modified version of the model, the
jitter was accounted for by using instead
n
P180 ¼ 2
n
^ ^b
Acknowledgements. This work was supported by grants from the NIH (to C.E.C.) and the Human
Frontier Science Program (to H.A.-S.). We thank G. Gerstein, I. Nelken, E. W. Rubel, D. Sanes and I. Segev
for comments, and the NCI Biomedial Supercomputing Center at Frederick for computer resources and
technical help.
Correspondence and requests for materials should be addressed to C.E.C. (e-mail: [email protected]).
A prolactin-releasing
peptide in the brain
Shuji Hinuma*, Yugo Habata*, Ryo Fujii*, Yuji Kawamata*,
Masaki Hosoya*, Shoji Fukusumi*, Chieko Kitada*,
Yoshinori Masuo*, Tsuneo Asano†, Hirokazu Matsumoto*,
Masahiro Sekiguchi‡, Tsutomu Kurokawa*,
Osamu Nishimura†, Haruo Onda* & Masahiko Fujino*
* Discovery Research Laboratories I, Pharmaceutical Discovery Research Division,
† Pharmaceutical Research Division, and ‡ Pharmaceutical Development
Division, Takeda Chemical Industries Ltd, 10 Wadai, Tsukuba, Ibaraki 300-4293,
Japan
.........................................................................................................................
b Pðig syn ; bjg syn Þ
i;n j;n
i¼0 j¼0
Received 7 January; accepted 16 March 1998.
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Hypothalamic peptide hormones regulate the secretion of most
of the anterior pituitary hormones, that is, growth hormone,
follicle-stimulating hormone, luteinizing hormone, thyroidstimulating hormone and adrenocorticotropin1,2. These peptides
do not regulate the secretion of prolactin1,2, at least in a specific
manner, however. The peptides act through specific receptors,
which are referred to as seven-transmembrane-domain receptors
or G-protein-coupled receptors3–7. Although prolactin is important in pregnancy and lactation in mammals, and is involved in
the development of the mammary glands and the promotion of
milk synthesis8,9, a specific prolactin-releasing hormone has
remained unknown. Here we identify a potent candidate for
such a hormone. We first proposed that there may still be
unknown peptide hormone factors that control pituitary function
through seven-transmembrane-domain receptors. We isolated the
Nature © Macmillan Publishers Ltd 1998
NATURE | VOL 393 | 21 MAY 1998
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